Tony Blair will declare today that the Government will not be panicked into policy U-turns by Labour's drubbing in last week's elections.

The Prime Minister will echo Margaret Thatcher's warning that "the lady is not for turning" by saying he will not flinch from taking unpopular decisions that are for the long-term benefit of Britain.

But John Prescott, his deputy, issued a barely coded warning to Mr Blair yesterday when he described Labour's showing in the elections for local authorities and for the mayor of London as "a wake-up call". "We have to listen to people's concerns," he told the MSF union's conference in Harrogate. "We have to enthuse our voters. We have to show we are delivering."

As they began their inquest into Labour's "Black Thursday", senior cabinet ministers agreed that the Government could not afford to be "buffeted around" by the short-term problems that plagued John Major's administration.

Mr Blair will tell the Periodical Publishers Association today: "When we passionately believe something to be right for the country, we see it through for the long term whatever the short-term costs."

He will make clear ministers would stick to their guns over their controversial plans to partially privatise Britain's air traffic control service.But the Prime Minister will also give a nod in the direction of Labour's heartlands by stressing that tackling poverty remains a priority for the Government.

"If you are wealthy and privileged, Britain has always worked well for you," he will say. "We are changing the country to make it work for those without the breaks of birth or wealth, for those who can't survive the violent swings of boom and bust in the economy, for those who count on rising living standards not for luxuries but to make ends meet."

The "no U-turns" message was reiterated last night by Gordon Brown, the Chancellor, who said in a speech in London: "It is not by populist fixes...but by maintaining stability and seeing through long-term modernisation and principled reforms that we will achieve our goals for full employment, prosperity and social justice."

Mr Brown responded to anger over last month's 75p-a-week rise in the basic state pension by promising that a new tax credit would help old people with incomes just above the level at which they qualify for benefits.

But the Chancellor's tax credit scheme failed to impress Baroness Castle, the former Labour minister, who called for the basic pension to be raised in line with earnings rather than prices.